In accretion processes around black holes, pseudo-Newtonian potentials are defined for the the black hole geometry. For examples, the potentials defined by Paczynski-Wiita and Artemova et al. for Schwarzschild black holes.

For Schwarzschild black holes, we already have an exact potential suitable for test particles defined by (e.g., in Shapiro & Teukolsky) $$V_\mathrm{eff}=\sqrt{\left(1-\frac{2}{r}\right)\left(1+\frac{l^2}{r^2}\right)}$$

My Question: Why are pseudo-potentials used when we already have an exact form of the potential? Can't we apply the above potential for accretion processes around Schwarzschild black holes?

  • $\begingroup$ Just a guess: Isn't the exact potential assuming that one also parametrizes proper time properly? It might be that when doing accretion models this is cumbersome, and one uses potentials defined on simpler time slicings? $\endgroup$ Apr 16 '20 at 9:49

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